98 Partial fractions and Laplace transforms

$$f(s)=q(s)+\frac{r(s)}{h(s)}$$

where $r(s)/h(s)$ is strictly proper. Now by the fundamental theorem of algebra,

$$h(s)=b\prod _{j=1}^n{(s-{\lambda }_j)}^{m_j}$$

where the ${\lambda }_j\in 𝐂$ are distinct. Then by the usual partial fractions calculation, we look for coefficients $a_k$ such that

$$\frac{r(s)}{h(s)}=\sum _k\frac{a_{k,n_k}}{{(s-{\lambda }_k)}^{n_k}},$$

with integers $1\le n_k\le m_k$. The poles and coefficients are unique.